How paper sizing actually works

ISO 216 sizes are not arbitrary. The A series starts from A0, which is defined as exactly one square metre, and every size follows from a single constraint: the ratio of the long side to the short side must be the square root of two, so that halving the sheet produces two sheets of the same proportions.

That is why two A4 sheets side by side are exactly A3, and why folding A3 in half gives you A4 with no waste and no odd margin. The maths works out to A0 at 841 × 1189 mm, and each subsequent size halves the previous one’s long edge.

GSM and US basis weight are not the same kind of number

This is the part that trips people up. GSM is an absolute measurement: grams per square metre. A 300 gsm card weighs 300 grams per square metre no matter what shape it is cut into.

US basis weight is not absolute. It is the weight of 500 sheets at a base size that varies by paper grade — and each grade has its own traditional base sheet. So the same physical paper is described by different numbers depending on which trade it is sold into:

Grade	Base sheet (in)	Base area (in²)	Conversion from gsm
Bond / writing	17 × 22	374	lb = gsm ÷ 3.76
Book / text	25 × 38	950	lb = gsm ÷ 1.48
Cover	20 × 26	520	lb = gsm ÷ 2.70
Index	25.5 × 30.5	778	lb = gsm ÷ 1.81
Tag	24 × 36	864	lb = gsm ÷ 1.63

The underlying conversion is gsm = lb × 1406.5 ÷ base area. In practice: 110 lb cover is about 300 gsm, and 20 lb bond is about 75 gsm. They are the same paper stock described in two trade dialects.

A worked example

A client asks for “300 gsm card” and their printer quotes “110 lb cover”. Are they the same thing?

1. Cover base area is 20 × 26 = 520 in².
2. gsm = 110 × 1406.5 ÷ 520 = 297.5 gsm.
3. So yes — 110 lb cover and 300 gsm card are the same stock to within rounding.

Note that this tells you the weight, not the thickness. Two papers of identical gsm can differ noticeably in caliper because of bulk: a coated 300 gsm and an uncoated 300 gsm card will feel different and will matter differently if you are calculating a book spine.

Which sizes to reach for

• A4 (210 × 297 mm) — letters, invoices, most office printing.
• A5 (148 × 210 mm) — booklets, notepads, half-fold greetings.
• A3 (297 × 420 mm) — posters, proofs, two-up A4.
• SRA3 (320 × 450 mm) — the press sheet that exists so A3 artwork plus bleed, trim marks and grip fits on one sheet. It is not a finished size; it is a printing size.
• DL (110 × 220 mm) — the standard compliment-slip and third-of-A4 mailer.

Common questions

Why is A4 210 × 297 and not a rounder number?

Because 297 is 210 × √2, rounded to the nearest millimetre. The √2 ratio is the whole point of the series: it is the only ratio that survives being halved and keeps its proportions.

Does a heavier paper always print better?

No. Heavier stock feeds differently through some presses and can crack along folded edges — a 350 gsm card folded without scoring will often split. Heavier is not better; appropriate is better.

What is the difference between SRA3 and A3?

A3 is a finished size you can trim to; SRA3 is a press sheet slightly larger in both dimensions so the printed piece has room for bleed and the machinery has something to grip.